The theory of complex multiplication has proven to be an essential tool in number theory, mainly due to the connections with class field theory developed by Kronecker, Weber, Fricke, Hasse, Deuring, and Shimura, among others. Certain important results have been shown first in the case of complex multiplication. Thus, it is a natural question to find all the isomorphism classes of elliptic curve...

The theory of relativity links space and time to account for observed events in four-dimensional space. In this article we describe an alternative static state causal discrete modeling system using omniscient viewpoint dynamical systems that can express object relations the moment(s) they are observed. To do this, three key components required, including introduction independent object-relative...

1 AbstractA review of the recommendations in currently applicable version chapter “Sleep-related breathing disorders adults” guideline “Non-restorative sleep/sleep disorders” conducted by steering group identified a number and chapters requiring revision or updating light new scientific clinical evidence. These included selected on diagnosis (clinical examination, polysomnography, respiratory p...

We solve the problem of counting the total number of observable targets (persons, vehicles, etc.) in a region based on local counts performed by sensors which measure only the number of targets nearby and neither their identities nor any positional information. This theory is robust and accommodates ad hoc sensor networks and mobile robot sensors alike. Comments Reprinted from: Robert Ghrist, Y...

Down-beating positional nystagmus is typically associated with central nervous system disease. Anterior canal benign paroxysmal positional vertigo (AC-BPPV) can mimic down-beating positional nystagmus of central origin, particularly when it is bilateral. Factors that increase the probability of bilateral AC-BPPV include a history of bilateral multicanal BPPV, transient down-beating and torsiona...

This paper researches an AUV (Autonomous Underwater Vehicle) positioning method based on SINS (Strapdown Inertial Navigation System)/LBL (Long Base Line) tightly coupled algorithm. This algorithm mainly includes SINS-assisted searching method of optimum slant-range of underwater acoustic propagation multipath, SINS/LBL tightly coupled model and multi-sensor information fusion algorithm. Fuzzy c...

The human visual system has specialised mechanisms for encoding mirror-symmetry and for detecting symmetric motion-directions for objects that loom or recede from the observers. The contribution of motion to mirror-symmetry perception has never been investigated. Here we examine symmetry detection thresholds for stationary (static and dynamic flicker) and symmetrically moving patterns (inwards,...

Application telemetry refers to measurements taken from software systems assess their performance, availability, correctness, efficiency, and other aspects useful operators, as well troubleshoot them when they behave abnormally. Many modern observability platforms support dimensional models of signals where the are accompanied by additional dimensions used identify either resources described or...